What kinds of cosmic objects have been detected as X-ray emitters?

The short answer to this is: a large number of them! In our own Solar
System, for example, the Sun is the strongest emitter of X-rays.
The Sun was first
detected as an X-ray source as long ago as 1948, and it emits X-rays with a
typical luminosity or power output Lx of 1027
erg s-1 or
1011 Giga Watts (GW) in the soft X-ray (0.2 - 5 keV) band.
At Solar Maximum, the Sun's persistent Lx can reach 5 x
1027 erg s-1, while during a very large solar
flare, values of Lx >~ 2 x 1028
erg s-1 can be attained.

Other objects in our Solar System which have been detected as
apparent X-ray `emitters' (actually not intrinsic but due to the reflection
of solar X-rays from their surfaces
and/or charge exchange of their atmospheres with the highly ionized solar wind)
include the Moon, the planets Jupiter, Saturn, Venus, Earth and Mars, two
or three
of the moons of Jupiter, and the Io Plasma Torus, as well as a number of
comets.

In our Milky Way Galaxy, the brightest individual X-ray emitters, with
persistent X-ray luminosities
of up to 2 x 1038 erg s-1 which are 100 billion
(1011) times greater than that of the `Quiet' Sun, are the
X-ray binaries (XRBs). XRBs are close binary systems
in which one member is a neutron star or black hole that is accreting matter
from the other [normal] companion star, and in the process releasing enormous
amounts of energy, much of it in the X-ray band. If well-supplied with matter
from a donor, they can radiate
persistently at a maximum level called the Eddington Luminosity,
which is 1.3 x 1038 (M/Msun) erg s-1,
e.g., the XRB Sco X-1 has Lx ~
2 x 1038 erg s-1.

Almost every
type of star from the most massive Wolf-Rayet and OB stars to low-mass
M dwarf stars, single white dwarf and neutron stars, and even
some sub-stellar mass brown dwarfs, have been detected as X-ray sources,
with X-ray luminosities in the range from 1025 erg s-1,
e.g., low-activity very-low-mass stars and brown dwarfs such as
the M9 V ultra-cool dwarf star DENIS-P J104814.7-395606 (Stelzer et al.
2012, A&A, 537, A94), up to
1035 erg s-1, e.g., the colliding-wind massive binary
system Eta Carina (discussed in many papers by the HEASARC scientist
Mike Corcoran!).
Some types of extended objects, such as planetary nebulae,
H II regions, the Local Bubble, etc., have also been detected as X-ray
sources. The only types of stars that have
not been confirmed as intrinsic X-ray sources are the A-type stars,
cool white dwarf stars, and single red
(M-type) giant and supergiant stars.

Exploding stars can emit copious X-rays! Supernovae can reach
peak X-ray luminosities of 1041 erg s-1, e.g.,
SN 1998bw, and their remnants can have X-ray luminosities of up to 3 x
1037 erg s-1 for hundreds to thousands of years after
their formation, e.g., the Crab SNR. The nova outbursts triggered in
cataclysmic binary systems, where material transferred onto a white
dwarf companion eventually ignites in a thermonuclear runaway, can have peak
X-ray luminosities of up to about
1035 erg s-1.

The integrated current X-ray luminosity of
our entire Galaxy is estimated to be about 3 x 1039 erg
s-1 = 15 times the luminosity of the persistent XRB Sco X-1.
The supermassive black hole Sgr A* at the center of our Galaxy is
currently in a low-luminosity, very sub-Eddington state (Lx 35 erg s-1), but it is widely believed that
about a century ago its was much more luminous (Lx ~
3 x 1039 erg s-1 ~ current X-ray luminosity of
the entire Galaxy): see
Terrier et al. (2010, ApJ, 719, 143) for more details. If Sgr A* ever
were to get a sufficient supply of accreting matter and radiate at the
Eddington Limit for such a massive object (Lx ~ 5 x
1044 erg
s-1), it would far outshine every other object in the Sky in
X-rays as seen from the Earth, with the sole exception of the Sun!
Interestingly, a dense gas cloud is now nearing Sgr A* on a very
eccentric orbit, with perigalacticon predicted to occur in Summer 2013.
This is expected to produce a major outburst of Sgr A*, although
probably not to its Eddington luminosity! Stay tuned....

In the entire Universe, the most luminous X-ray sources are the
active
galactic nuclei (AGN), which can have X-ray luminosities of as high as
1047 erg s-1, and rich clusters of
galaxies, which can have
X-ray luminosities of up to about 3 x 1045 erg s-1.
Typical individual `normal' galaxies, on the other hand, have much lower X-ray
luminosities in the range from 1038
erg s-1 to 3 x 1042 erg s-1.